Find the standard equation for the circle with center on the negative y -axis and passing through the origin with radius of 3.

A. x^2 + y^2 = 9
B. (x + 3)^2 + y^2 = 9
C. x^2 + (y + 3)^2 = 9

The correct option is C : x² + (y +3)² = 9 .

Step-by-step explanation:

We know that the general equation for a circle is ( x - h )² + ( y -k )²= r², Where,

Let the point be ( 0 , -y) , since it is on negative y axis . And the circle passes through the origin that is (0,0) . Hence the center will be 3 units down the y - axis that is ( 0 , -3) .Hence h will be 0 and y = (-3) .

Now its given that the radius of the circle is 3. So on substituting r = 3 , in standard form we have ,

⇒ ( x -h )² + ( y - k )²= r²

⇒ ( x - 0)² + { y - (-3) }² = 3²

⇒ x² + ( y + 3) ² = 3²

⇒ x² + ( y + 3)² = 9

Note that I have attached the graph of the same .

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step-by-step explanation:

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step-by-step explanation: